9.4 Short-Run SPC and Moving Average Charts

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1 Chapter 1: Introduction & CSSBB Exam Strategy

1.1 CSSBB Exam Format, Scoring, and Testing Windows 1.2 Eligibility, Project Affidavits, Application, and Recertification 1.3 Open-Book Strategy, Reference Materials, and a 16-Week Study Plan

2 Chapter 2: Organization-Wide Planning and Deployment

2.1 Fundamentals of Six Sigma and Lean Methodologies 2.2 Selecting the Right Methodology: DMAIC, DFSS, and Lean 2.3 Business Systems, Processes, and Stakeholder Relationships 2.4 Strategic Planning and Deployment of Six Sigma Initiatives 2.5 Six Sigma Roles and Responsibilities 2.6 Organizational Barriers and Common Causes of Six Sigma Failure 2.7 Change Management: Stakeholder Analysis, Readiness, and Communication

3 Chapter 3: Organizational Process Management and Measures

3.1 Impact of Six Sigma Projects on Customers, Suppliers, and Stakeholders 3.2 Benchmarking Types and Performance Goal Setting 3.3 Performance Measures: Balanced Scorecard, KPIs, KBIs, OKRs, and Line of Sight 3.4 Leading and Lagging Indicators and Performance Dashboards 3.5 Financial Measures: Revenue Growth, Margin, NPV, ROI, and Cost-Benefit Analysis 3.6 Cost of Poor Quality and Hard versus Soft Savings

4 Chapter 4: Team Management

4.1 Team Types and Constraints 4.2 Team Roles, Responsibilities, and Member Selection 4.3 Team Success Factors and Ground Rules 4.4 Motivational Techniques and Overcoming Demotivators 4.5 Stages of Team Development and Conflict Resolution 4.6 Team Communication Plans 4.7 Team Leadership Models: Direct, Coach, Support, and Delegate 4.8 Group Behaviors, Conflict Resolution, and Meeting Management 4.9 Facilitation Techniques and Team Decision-Making Methods 4.10 Team Training: Needs Assessment, Delivery, and Evaluation

5 Chapter 5: Define Phase

5.1 Customer Identification and Segmentation 5.2 Customer Data Collection: Methods, Validity, and Reliability 5.3 Customer Requirements: CTX, CTQ Trees, and Operational Definitions 5.4 The Kano Model and Quality Function Deployment 5.5 SIPOC and Process Mapping 5.6 Business Case Justification 5.7 The Project Charter and the Problem Statement 5.8 Project Scope and Boundaries 5.9 SMART Goals and Project Performance Measurements 5.10 Project Charter Reviews and Toll-Gate Governance 5.11 Project Management Tools: Gantt Charts, Toll-Gate Reviews, WBS, and RACI 5.12 Analytical Tools Used Throughout the DMAIC Cycle

6 Chapter 6: Measure Phase

6.1 Process Flow Metrics and the Hidden Factory 6.2 Process Analysis Tools and Value Stream Mapping 6.3 Types of Data and Measurement Scales 6.4 Sampling Concepts, Methods, and Sample Size for Estimation 6.5 Data Collection Plans and Common Pitfalls 6.6 Gage R&R for Variable Measurement Systems 6.7 Attribute Agreement Analysis and Audit MSA 6.8 Measurement Systems Across the Organization, and Metrology 6.9 Population Parameters, Sample Statistics, and Valid Statistical Conclusions 6.10 Descriptive Statistics: Central Tendency, Dispersion, and Shape 6.11 Graphical Methods for Exploratory Data Analysis 6.12 Probability Concepts, Common Distributions, and the Central Limit Theorem 6.13 Additional Distributions: Hypergeometric, Exponential, Lognormal, Weibull, and Bivariate 6.14 Process Capability and Performance Indices 6.15 Capability Studies, Attributes Capability, Yield Metrics, and Long-Term Capability

7 Chapter 7: Analyze Phase

7.1 The Correlation Coefficient, Its Confidence Interval, and Causation 7.2 Linear Regression and Residual Analysis 7.3 Multivariate Tools: Factor Analysis, Discriminant Analysis, and MANOVA 7.4 Hypothesis Testing Terminology, Errors, and Single-Sample Tests 7.5 Statistical Versus Practical Significance 7.6 Sample Size for Hypothesis Tests 7.7 Point Estimates, Confidence, Prediction, and Tolerance Intervals 7.8 Tests for Means, Variances, and Proportions 7.9 Analysis of Variance 7.10 Chi-Square Goodness-of-Fit and Tests of Independence 7.11 Types of Risk and Failure Mode and Effects Analysis 7.12 Gap Analysis and Root Cause Analysis 7.13 Waste Analysis: The Seven Classic Wastes and Resource Under-Utilization

8 Chapter 8: Improve Phase

8.1 Design of Experiments: Objectives, Terminology, and Effects 8.2 DOE Design Principles: Randomization, Blocking, Replication, and Resolution 8.3 Planning and Evaluating Designed Experiments 8.4 One-Factor Experiments: Completely Randomized, Randomized Block, and Latin Square Designs 8.5 Full Factorial Experiments and Design Selection 8.6 Two-Level Fractional Factorial Experiments and Confounding 8.7 Response Surface Methodology and Optimization 8.8 Waste Elimination: Pull Systems, Kanban, 5S, and Poka-Yoke 8.9 Cycle-Time Reduction: Continuous Flow, SMED, and Heijunka 8.10 Kaizen, Kaizen Blitz, Theory of Constraints, and OEE 8.11 Implementation Planning, Piloting, and Solution Selection

9 Chapter 9: Control Phase

9.1 SPC Objectives, Variable Selection, and Rational Subgrouping 9.2 Control Charts for Variables Data 9.3 Control Charts for Attributes Data 9.4 Short-Run SPC and Moving Average Charts 9.5 Control Chart Analysis: Common Cause, Special Cause, and Run Rules 9.6 Total Productive Maintenance and Visual Controls 9.7 Measurement System Reanalysis 9.8 Control Plan Development and Process Owner Handoff 9.9 Lessons Learned, Documentation, and Training for Sustainment 9.10 Ongoing Evaluation of the Improved Process

10 Chapter 10: Design for Six Sigma (DFSS)

10.1 DFSS Frameworks: DMADV, DMADOV, and Design Transfer 10.2 Design for X (DFX) 10.3 Robust Design, Parameter Design, and Verification 10.4 Tolerance Design and Statistical Tolerancing

9.4 Short-Run SPC and Moving Average Charts

Key Takeaways Explain This Topic AI

Short-run SPC transforms measurements into a common dimensionless scale so parts with different targets can share one chart.

The DNOM chart plots deviation from nominal and requires the parts to share a common process standard deviation.

The standardized Z chart divides deviation from nominal by the part's own standard deviation and removes the common-variance requirement.

A Shewhart chart uses only the current subgroup, so it is slow to detect small sustained shifts; EWMA and CUSUM accumulate history and detect them quickly.

The EWMA smoothing constant lambda trades sensitivity to small shifts against responsiveness to large ones.

Last updated: August 2026

• The short-run problem
• A conventional X-bar and R chart needs roughly 20 to 25 subgroups to establish trustworthy limits. A job
• shop that runs 30 pieces of a part number and then changes over never accumulates them, and it may
• never run that part again. Yet the process -- the machine, the operator, the method -- is continuous

even though the parts are not.

Short-run SPC solves this by charting the process rather than the part, transforming each

measurement onto a common scale so that different part numbers can be plotted on one chart.

The DNOM chart

Deviation from nominal subtracts each part's own target from its measurement: x D N O M = x m e a s u r e d − Target p a r t x_{DNOM} = x_{measured} - \text{Target}_{part} x D NOM ​ = x m e a s u re d ​ − Target p a r t ​

All part numbers then plot around a common centre line of zero, and standard X-bar and R limits apply to

the transformed values.

Worked example. Three part numbers on one lathe:

• Part Target (mm) Measured (mm) DNOM
• A-100 25.00 25.03 +0.03
• A-100 25.00 24.98 -0.02
• B-220 40.00 40.04 +0.04
• B-220 40.00 39.99 -0.01
• C-315 12.50 12.52 +0.02
• All five points plot on one chart around zero, and the chart now monitors the lathe's ability to hold

nominal regardless of what it is making.

• Requirement : the parts must share approximately the same process standard deviation . If part
• C-315 is turned to a much tighter tolerance with a different feed and speed, its variation will differ

from A-100's and pooling them on one DNOM chart produces limits that are wrong for both.

The standardized Z chart

When the parts do not share a common standard deviation, standardize as well as centre: Z = x − Target p a r t σ ^ p a r t Z = \frac{x - \text{Target}_{part}}{\hat{\sigma}_{part}} Z = σ ^ p a r t ​ x − Target p a r t ​ ​

• Now every point is expressed in the part's own standard deviations, so the chart has a centre line of 0
• and limits at ± 3 \pm 3 ± 3 regardless of the part or even the unit of measurement. A diameter in millimetres

and a hardness in HRC can share one chart.

• DNOM chart Standardized Z chart
• Transformation Subtract target Subtract target, divide by part sigma
• Requires common sigma Yes No
• Requires historical sigma per part No Yes
• Units on the chart Original units Dimensionless
• Interpretation Direct, in engineering units Requires back-conversion
• The Z chart's cost is that it needs a prior estimate of sigma for every part number . For a brand-new
• part with no history, an engineering estimate or a pooled estimate from similar parts is used, and the

chart is provisional until data accumulates.

Related short-run tools include the target X-bar and R chart (target lines drawn per part on a

common chart) and short-run attribute charts that standardize proportions the same way.

• Why Shewhart charts are slow to small shifts
• A Shewhart chart makes its decision from the current subgroup only. Its average run length to detect

a shift of size k σ k\sigma kσ in the subgroup mean is roughly:

• Shift size ARL to detect (X-bar chart, 3 sigma limits, no run rules)
• 0.5 σ 0.5\sigma 0.5 σ about 155 subgroups
• 1.0 σ 1.0\sigma 1.0 σ about 44 subgroups
• 1.5 σ 1.5\sigma 1.5 σ about 15 subgroups
• 2.0 σ 2.0\sigma 2.0 σ about 6 subgroups
• 3.0 σ 3.0\sigma 3.0 σ about 2 subgroups
• A sustained half-sigma shift takes on average 155 subgroups to trigger a point beyond a control limit --
• weeks or months of production. Run rules (such as eight points on one side of the centre line) improve
• this considerably, but the fundamental limitation remains: a chart that looks only at the newest point

throws away the information in the previous ones.

• Moving average and EWMA charts
• Simple moving average

Plots the average of the last w w w observations: M A t = x t + x t − 1 + ⋯ + x t − w + 1 w , σ M A = σ w MA_t = \frac{x_t + x_{t-1} + \cdots + x_{t-w+1}}{w}, \qquad \sigma_{MA} = \frac{\sigma}{\sqrt{w}} M A t ​ = w x t ​ + x t − 1 ​ + ⋯ + x t − w + 1 ​ ​ , σ M A ​ = w ​ σ ​

• Averaging suppresses noise, so small sustained shifts become visible. The costs are that consecutive
• points are correlated (they share observations), which makes run rules invalid, and that the chart lags

a real change by up to w w w periods.

Exponentially weighted moving average

EWMA weights all past observations, with weights decaying geometrically: z t = λ x t + ( 1 − λ ) z t − 1 , z 0 = μ 0 z_t = \lambda x_t + (1 - \lambda) z_{t-1}, \qquad z_0 = \mu_0 z t ​ = λ x t ​ + ( 1 − λ ) z t − 1 ​ , z 0 ​ = μ 0 ​

with control limits μ 0 ± L σ λ 2 − λ [ 1 − ( 1 − λ ) 2 t ] \mu_0 \pm L\sigma\sqrt{\frac{\lambda}{2 - \lambda}\left[1 - (1-\lambda)^{2t}\right]} μ 0 ​ ± L σ 2 − λ λ ​ [ 1 − ( 1 − λ ) 2 t ] ​

which widen from a narrow start and converge to a steady-state value.

• λ \lambda λ Behaviour
• 0.05 - 0.10 Very heavy smoothing; excellent for very small shifts; slow on large ones
• 0.20 - 0.30 Common general-purpose range
• 1.00 Reduces exactly to a Shewhart individuals chart

Typical settings are λ = 0.2 \lambda = 0.2 λ = 0.2 with L = 3 L = 3 L = 3 , or λ = 0.1 \lambda = 0.1 λ = 0.1 with L = 2.7 L = 2.7 L = 2.7 . The trade-off is

explicit: small λ \lambda λ means more memory, so small shifts are found faster and large shifts more

slowly.

CUSUM

The cumulative sum chart accumulates deviations from target: C i + = max ⁡ [ 0 , x i − ( μ 0 + K ) + C i − 1 + ] , C i − = max ⁡ [ 0 , ( μ 0 − K ) − x i + C i − 1 − ] C_i^{+} = \max\left[0,\; x_i - (\mu_0 + K) + C_{i-1}^{+}\right], \qquad C_i^{-} = \max\left[0,\; (\mu_0 - K) - x_i + C_{i-1}^{-}\right] C i + ​ = max [ 0 , x i ​ − ( μ 0 ​ + K ) + C i − 1 + ​ ] , C i − ​ = max [ 0 , ( μ 0 ​ − K ) − x i ​ + C i − 1 − ​ ]

with a signal when either statistic exceeds the decision interval H H H . Conventional settings are K = 0.5 σ K = 0.5\sigma K = 0.5 σ (half the shift to be detected) and H = 5 σ H = 5\sigma H = 5 σ .

CUSUM and EWMA have similar performance and are chosen largely by preference; EWMA is easier to plot and

explain, CUSUM has a slightly more direct interpretation of the shift magnitude.

Choosing a chart

• Situation Chart
• High-volume, single part, detect large shifts X-bar and R or X-bar and s
• Individual measurements, single part Individuals and moving range
• Many part numbers, short runs, similar variation DNOM
• Many part numbers, short runs, different variation Standardized Z
• Need to detect a sustained shift of 1 sigma or less quickly EWMA or CUSUM
• Autocorrelated process data such as chemical batch EWMA on residuals from a time-series model
• A practical combination is a Shewhart chart plus an EWMA on the same data : the Shewhart chart catches
• large sudden shifts and supports run rules, and the EWMA catches the slow drift the Shewhart chart would

take months to find.